Frasen was arrested in London by Irish police November 19 for "threatening, abusive or insulting words or behavior" displayed at a rally in Belfast, Ireland, in August.
It's unclear whether Frasen, 31, who is deputy leader of the Britain First party, is now running the account.
After sharing the posts with his 43.6m Twitter followers, Mr Trump fired off three other tweets praising the U.S. stock market, suggesting a boycott of "fake news CNN" and commenting on the sacking of NBC presenter Matt Lauer.
The posts included unverified videos titled "Muslim Destroys a Statue of Virgin Mary!" and "Muslim migrant beats up Dutch boy on crutches!"
The first video, which Fransen claimed shows a Muslim migrant attacking a Dutch man on crutches, was also shared by one of Mr Trump's most vocal supporters, conservative commentator Ann Coulter.
In September, its leader Paul Golding, 35, and deputy Fransen, 31, were charged with causing religiously aggravated harassment after distributing leaflets and posting videos to social media during the gang rape trial of three Muslim men and a teenager who were later convicted of rape and imprisoned.
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Fransen reacted jubilantly online, touting that the videos had been shared with Trump's almost 44 million followers.
Britain first is a far-right ultranationalism group which purports to document Muslim activity across Britain and Europe.
The retweets were met with criticism on Twitter. "Spreading hatred has consequences and the president should be ashamed of himself".
Britain First, which claims to have a Christian ideology, responded to the Trump retweets of its deputy leader.
The other two videos appear in Fransen's timeline but not in sequence.